Reconstruction of volume data with quadratic super splines

Rössl, Christian; Seidel, Hans Peter; Zeilfeider, F.; Nürnberger, Günther

doi:10.1109/tvcg.2004.16

Cited by 35 publications

(41 citation statements)

References 38 publications

(61 reference statements)

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“…The quadratic triangular B-spline surface [8] is composed of the surface patches of separate triangles of the triangulation τ , which are calculated using TBS of the degree 2. Then points of the quadratic triangular B-spline patch for a triangle I = {t 00 , t 10 , t 20 } are calculated as follows…”

Section: Calculation Of Quadratic Triangular B-spline Surfacementioning

confidence: 99%

Generation of Knot Net for Calculation of Quadratic Triangular B-spline Surface of Human Head

Mihalik¹

2011

Journal of Electrical Engineering

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This paper deals with calculation of the quadratic triangular B-spline surface of the human head for the purpose of its modeling in the standard videocodec MPEG-4 SNHC. In connection with this we propose an algorithm of generation of the knot net and present the results of its application for triangulation of the 3D polygonal model Candide. Then for the model and generated knot net as well as an established distribution of control points we show the results of the calculated quadratic triangular B-spline surface of the human head including its textured version for the texture of the selected avatar.K e y w o r d s: triangular B-spline, quadratic surface, knot net, human head, 3D polygonal model

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Section: Calculation Of Quadratic Triangular B-spline Surfacementioning

confidence: 99%

Generation of Knot Net for Calculation of Quadratic Triangular B-spline Surface of Human Head

Mihalik¹

2011

Journal of Electrical Engineering

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“…Regular grids with trilinear reconstruction have been considered in [13], second-order splines in [15], second-order tetrahedras in [23][24][25] as well as spectral/hp elements in [11].…”

Section: Related Workmentioning

confidence: 99%

Second Order Pre-Integrated Volume Rendering

Hajjar

Marchesin

Dischler

et al. 2008

2008 IEEE Pacific Visualization Symposium

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In the field of Volume Rendering, pre-integration techniques for arbitrary transfer functions has certainly led to the most significant and convincing results both quality and performance wise on standard PC consumer graphics. By showing that the ideal scalar signal along the cast rays is better approximated by a succession of polynomial curves as opposed to linear segments, we propose a new method for pre-integrated volume rendering. This method is based on a second order polynomial interpolation of the scalar values, allowing it to converge more rapidly towards the integration of a volume reconstructed by a trilinear filter. This approach manages to capture the smoothness of the volume's details without the need of further ray resampling, and consequently succeeds in reducing the visual artefacts in comparison to previous techniques. Futhermore, we adapt an existing technique to compute our pre-integration tables using the GPU, thus making our approach suitable for transfer function manipulations.

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“…Except for the spaces discussed in [29], all of these constructions require Hermite data, and cannot be modified to work with Lagrange data. Recently, some local quasi-interpolation methods that are based on trivariate splines and require only Lagrange data have been constructed; see [20], [27], [33]. These methods differ from the method discussed here in that no data is interpolated.…”

Section: Lemma 81 Fix F ∈ C(ω) and Let T Be A Tetrahedron In Supmentioning

confidence: 99%

A local Lagrange interpolation method based on $C^{1}$ cubic splines on Freudenthal partitions

et al. 2007

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Abstract. A trivariate Lagrange interpolation method based on C 1 cubic splines is described. The splines are defined over a special refinement of the Freudenthal partition of a cube partition. The interpolating splines are uniquely determined by data values, but no derivatives are needed. The interpolation method is local and stable, provides optimal order approximation, and has linear complexity. §1. Introductionbe a set of points in R 3 . In this paper we are interested in the following problem. Problem 1. Find a tetrahedral partition whose set of vertices includes V, an Ndimensional space S of trivariate splines defined on with a prescribed smoothness r, and a set of additional points {η i } N i=n+1 such that for every choice of the data, there is a unique spline s ∈ S satisfying (1.1)We call P :and S a Lagrange interpolation pair. It is easy to solve this problem using C 0 splines; see Remark 1. In this case no additional interpolation points are needed. However, the situation is much more complicated if we want to use C r splines with r ≥ 1. For r = 1 the problem was first solved in [29] for the special case where the points in V are the vertices of a cube partition. The method uses quintic splines, and provides full approximation power six for sufficiently smooth functions. In [23] we recently described two C 1 methods which solve the problem for arbitrary initial point sets V. The first method is based on quadratic splines, and requires that each tetrahedron be split into 24 subtetrahedra. The second method is based on cubic splines, and requires that each tetrahedron be split into 12 subtetrahedra. Both methods provide approximation order three for sufficiently smooth functions. For the quadratic spline case this is the optimal approximation order, but for the cubic case it is suboptimal.The aim of this paper is to describe a new method based on cubic C 1 splines which yields optimal approximation order four. To achieve this, we restrict ourselves

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Reconstruction of volume data with quadratic super splines

Cited by 35 publications

References 38 publications

Generation of Knot Net for Calculation of Quadratic Triangular B-spline Surface of Human Head

Generation of Knot Net for Calculation of Quadratic Triangular B-spline Surface of Human Head

Second Order Pre-Integrated Volume Rendering

A local Lagrange interpolation method based on $C^{1}$ cubic splines on Freudenthal partitions

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